A power transmitting apparatus is largely divided into a rack and pinion for converting a rotational motion to a linear motion or vice versa and a gear train for transmitting only a rotational motion while converting a rotational speed and a torque. Typically, a power transmitting system of a power transmitting apparatus mainly uses a tooth shape according to an involute curve principle. However, there is a rare case of using a tooth shape according to a cycloid curve principle and a pin gear.
FIGS. 1 and 2 illustrate the structure of a part of a rack and pinion using an involute tooth shape according to a related art.
When a pre-load is applied to a rack and pinion using an involute tooth shape as illustrated in FIG. 1, a tooth J4 of a pinion J3 is forcibly inserted between teeth J2 of a rack J1 and contacts the teeth J2 so that a large frictional force is generated and thus efficiency is remarkably deteriorated.
Thus, at a stage of design, as illustrated in FIG. 2, a backlash that is a gap between the tooth J2 and the tooth J4 is formed to avoid a phenomenon that the tooth J4 of the pinion J3 is forcibly inserted between the teeth J2 of the rack J1.
However, when the backlash is formed as illustrated in FIG. 2, transfer or a motion is not smoothly performed, that is, a motion is transferred intermittently from the tooth J2 to the tooth J4, so that noise or vibration is generated. Further, the gears may rattle during a reverse motion.
FIG. 3 illustrates the structure of a part of a rack and pinion using a cycloid curve. FIG. 4 illustrates an undercut of FIG. 3. FIG. 5 is a structural view of FIG. 4. FIG. 6 illustrates a state in which a pre-load is applied in FIG. 3.
As a solution to solve the problem of the above-described involute tooth shape, as illustrated in FIG. 3, a rack and pinion in which a pin J5 in a roller form is used as the tooth J4 of the pinion J3 (see FIG. 1) and the teeth J2 of the rack J1 have a tooth shape formed of a cycloid curve may be taken into consideration.
According to the track and pinion of FIG. 3, since the pin J5 revolves, that is, the pin J5 performs a rolling motion, and moves on a tooth surface of the rack J1 to transfer a motion, transfer resistance is low. Further, several of the pins J5 are simultaneously engaged with several of the teeth J2 so that the motion may be continuously transferred and the rattling during reverse transfer may be prevented.
However, in the tooth J2 of the rack J1 according to the cycloid curve, when the pin J5 arrives at a tooth root J6, a radius of curvature of a central track of the pin J5 becomes zero so that, during the processing of the part of the rack J1, an undercut A such as a hatched portion in FIG. 4 may be problematic.
The undercut A may not be problematic when used for an apparatus that does not require precision. However, as illustrated in FIG. 5, it may be problematic when the undercut A is applied to an apparatus requiring high precision such as a precision mechanism because the pin J5 escapes from the tooth J2 of the rack J1 and does not follow a predetermined cycloidal track, thus failing to transfer a torque.
Further, as the escape and engagement of the pin J5 with respect to the tooth J2 of the rack J1 due to the undercut A, noise and vibration are generated so that life span of a tooth surface may be deteriorated.
In addition, as described above, in the tooth J2 of the rack J1 according to the cycloid curve in FIG. 3, when the pin J5 arrives at the tooth root J6, the radius of curvature of a central track of the pin J5 becomes zero and thus the diameter of the pin J5 matches the diameter of the tooth root J6. Accordingly, when the pin J5 arrives at the tooth root J6, about half of the outer circumference of the pin J5 closely contacts the tooth root J6 so that the pin J5 may be not rotated.
Thus, the pin J5 repeats rotation and stop at a portion around the tooth root J6 and also the pin J5 bumps against the tooth root J6 so that noise and vibration are generated. In particular, when a pre-load is applied between the rack J1 and the pinion J3 after removing backlash to improve rigidity, the above-described problem is severely generated.
As a result, in the tooth J2 of the rack J1 according to the cycloid curve, as described above, since the undercut A is generated, when the number of the pin J5 is small, a plurality of teeth J2 may not be always engaged. Also, in this area, a backlash in forward and reverse directions is inevitably generated, which has been disregarded until now.
Alternatively, a method of applying a pre-load between the rack J1 and the pinion J3 in order to remove a backlash that is a gap between the tooth J2 and the pin J5 may be taken into consideration. According to this method of applying a pre-load, since a force is applied to surfaces of the pin J5 and the tooth J2, no gap exists and initial twist of a part may be prevented so that rigidity may be greatly improved.
The tooth shape according to the cycloid curve is obtained by adding the radius of the pin J5 to a track (cycloid curve) drawn by the center of the pin J5 when the pinion J3 rolls. Thus, based on this fact, the tooth shape according to the cycloid curve has been reported as one being theoretically capable of smoothly transferring power by rolling contact.
Yet, when a pre-load is applied between the rack J1 and the pinion J3, as illustrated in FIG. 6, bump and release are made as much as the pre-load during engagement start and escape of the tooth J2 of the rack J1 and the pin J5 so that noise or vibration due to the bump and release may be generated. In particular, the bump and release causes fatigue of the pin J5 or the tooth J2 so that life span of the rack and pinion may be deteriorated.
In the above structure of the rack and pinion, to avoid the undercut of the tooth root portion and the pin and tooth forcibly insertion phenomenon that are generated when a pre-load is applied to the pin gear and the tooth gear corresponding thereto and the tooth shape of a cycloid curve of FIG. 3 is applied to the tooth shape of the tooth gear, a method of changing the tooth shape to a trochoid tooth shape may be suggested.
However, the trochoid tooth shape may have problems that reduction of a tooth size (tooth width and tooth height), reduction of a tooth shape contact rate due to reduction of a power transfer area of one tooth, remarkable deterioration of rigidity due to reduction of thickness in a tooth root portion, and shortening of life span of a pin support bearing due to an increase in a normal force applied to each pin gear during the application of the same torque due to a decrease of a pitch diameter of a pin gear by electrostatic potential.
Therefore, there is a demand for a method to solve a pin stuck phenomenon and reduction of a tooth thickness due to the undercut of a tooth root portion while a cycloid tooth shape having a tooth size higher than a trochoid tooth shape and capable of maintaining a sufficient tooth contact rate is applied to a tooth shape of a tooth gear engagingly coupled to a pin gear capable of relatively moving.